Author

Chang-Xing Miao

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Preprint Oct 2026

Improved $L^p$ maximal estimates for higher-degree Weyl sums

For each integer $k\ge3$, we establish the following estimate for all $1\le p<\infty$ and $\varepsilon>0$: \[ \left\|\sup_{t\in\mathbb{T}}\left|\sum_{n=1}^N e(nx+n^kt)\right|\right\|_{L^p(\mathbb{T})} \ll_{k,p,\varepsilon} N^{\max\{1-1/K_k,\,1-1/p\}+\varepsilon}, \] where $K_k=\min\{2^{k-1},k(k+1)/2\}$, $e(z)=e^{2\pi i...

Xue-Zhi Chen, Chang-Xing Miao, Ji-Ye Yuan et al. · 0 citations

Preprint Oct 2026

Endpoint Mapping Properties of Wave Operators for Schr\"odinger Operators in Dimensions $n\ge3$

We study endpoint mapping properties of low-energy wave operators for Schr\"odinger operators $H=-\Delta+V$ on $\mathbb R^n$, $n\ge3$. In dimension four, we prove that a zero-energy resonance prevents $L^1$ boundedness, whether or not zero is also an eigenvalue, under $|V(x)|\lesssim\langle x\rangle^{-\beta}$ with $\be...

Han Cheng, Chang-Xing Miao, Xiao-Hua Yao · 0 citations

Preprint Aug 2026

Endpoint Mapping Properties of Wave Operators for Two-Dimensional Schr\"odinger Operators

We establish sharp endpoint mapping properties for the wave operators $W_\pm(H,-\Delta)$ of two-dimensional Schr\"odinger operators $H=-\Delta+V$ with real-valued decaying potentials $V$. Together with the known non-endpoint $L^p$ theory, our results give a complete classification of the $L^p$ mapping properties of the...

Han Cheng, Chang-Xing Miao, Xiao-Hua Yao · 1 citation